CN107167306B - Order extraction-based rotating machine rotor running state modal analysis method - Google Patents
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Abstract
The embodiment of the invention discloses a rotating machinery rotor running state modal analysis method based on order extraction, and relates to the field of vibration signal processing and system parameter identification. The method can avoid harmonic interference generated by the rotor of the rotary machine in a working state, so that the reliability of modal parameter identification is improved. The method is suitable for identifying the vibration mode parameters of the rotor of the rotary machine in the running state. The method of the invention comprises the following steps: extracting an order vibration signal of a rotor of the rotating machine in an operating state based on an order ratio tracking algorithm of instantaneous frequency estimation; and carrying out modal parameter identification on the extracted signals by using a modal identification algorithm.
Description
Technical Field
The invention relates to the field of rotor vibration signal processing and rotor modal parameter identification, in particular to the field of vibration modal analysis in an operating state.
Background
The vibration mode analysis is an indispensable means for acquiring the dynamic characteristics of the mechanical structure, and is the basis of vibration control, structure state monitoring, vibration and noise reduction, mechanical structure fault diagnosis, finite element model correction and confirmation. At present, the main methods are: finite element method, traditional test mode analysis method based on input and output mode data and operation state mode analysis method based on only output data. The finite element method has a remarkable advantage for solving a rotating mechanical problem formed by the rotor and the surrounding structure together. However, in practical engineering, due to the influence of uncertain factors such as complex boundary conditions of the structure, physical parameters of the structure, connection states of components and the like, it is difficult to establish an accurate finite element model.
The traditional test mode analysis is usually completed in a laboratory, the test state is easy to control, and the measurement signal-to-noise ratio is high. The test mode analysis of the rotary machine mainly carries out mode test in a non-working state, and due to the lack of influences of factors such as gyro moment and the like, the test result of the rotary machine is possibly greatly different from the test result in a running state. The traditional operation state modal analysis method generally requires that a structure is under the action of an excitation force with broadband characteristics, and for a rotating machine, the operation of each rotating part causes harmonic components closely related to the rotating speed, so that great difficulty is caused in identifying structural modal parameters.
Disclosure of Invention
In order to solve the problems in the prior art, embodiments of the present invention provide a method for analyzing a rotor operating state mode based on order extraction, which can avoid harmonic interference caused by rotational excitation and improve accuracy of mode parameter identification in an operating state of a rotating machine.
In order to achieve the purpose, the implementation of the invention adopts the following technical scheme:
in a first aspect, an embodiment of the present invention provides an adaptive Vold-Kalman filtering order tracking technique based on instantaneous frequency estimation, where the method is used for rotor operation state vibration signal processing, and the method includes:
aiming at the rotor vibration signal, calculating the rotor speed by using an instantaneous frequency estimation method;
and calculating to obtain a certain order signal by combining the self-adaptive Vold-Kalman filtering order ratio tracking technology according to the rotating speed.
In a second aspect, an embodiment of the present invention provides a rotor modal analysis method combining an adaptive filtering order ratio tracking technique with a modal identification algorithm, the method is used for identifying modal parameters of a rotor, the rotor system is inconvenient to apply excitation in an operation state, and in a case of response only, the method includes:
directly performing power spectrum analysis on the extracted certain order signal, and performing singular value decomposition on the power spectrum to obtain a left singular vector and a right singular vector;
and calculating to obtain an enhanced power spectrum according to the left singular vector and the right singular vector, and calculating the damping and the natural frequency by using the enhanced power spectrum.
Compared with other order tracking algorithms at present, the adaptive filtering order tracking technology based on instantaneous frequency estimation provided by the invention does not need to install hardware equipment to measure the rotating speed signal, and the workload is greatly reduced. In addition, the embodiment also provides a rotor modal analysis method combining the adaptive filtering order ratio tracking technology and the frequency domain spatial domain decomposition method, which has the advantages of being less in workload, less in calculation amount and high in operation speed under the conditions that excitation is inconvenient to apply or unknown and only response is available.
Drawings
FIG. 1 is a flow chart of an algorithm of the present invention for identifying structural modal parameters of a rotor of a rotating machine;
FIG. 2 is a waterfall diagram of the original signals of the rotor;
FIG. 3 is a time domain comparison of a rotor raw signal and an extracted 2X signal;
FIG. 4 is a waterfall plot of the 2X signal;
FIG. 5 is a modal indication plot of a 2X signal;
FIG. 6 illustrates the algorithm of the present invention identifying the first three bending modes of the rotor.
Detailed Description
The embodiment of the invention provides a rotating machinery rotor running state modal analysis method based on order extraction, which can avoid harmonic interference caused by rotation excitation, thereby improving the accuracy of modal parameter identification in the rotating machinery running state.
To achieve the above object, as shown in fig. 1, the present invention is implemented by the following steps:
the method comprises the following steps: performing time-frequency analysis on the time domain signal to draw a waterfall graph;
step two: estimating the rotating speed of the rotating shaft by an instantaneous frequency estimation method;
step three: the self-adaptive Vold-Kalman filtering order ratio tracking algorithm is used for extracting the order of a signal of a certain order;
step four: and analyzing the modal parameters of the extracted order signals by using a frequency domain space domain decomposition (FSDD) method.
In the first step, time-frequency analysis is performed on the time domain signal, as shown in fig. 2, a specific method for drawing a waterfall graph is as follows:
and performing STFT on the time domain vibration signal to obtain a time-frequency spectrogram, wherein order components can be observed from the time-frequency spectrogram, so that order extraction in the following steps is facilitated.
The concrete method for estimating the rotating speed of the rotating shaft by the instantaneous frequency estimation method in the step two is as follows:
as shown in fig. 3 and 4, a Short-Time fourier transform (STFT) is performed on the vibration signal to obtain a Time-frequency spectrum, and since the frequency corresponding to the highest spectral peak energy density is most likely to be the instantaneous rotation frequency, the maximum value of the spectral peak energy density in the Time-frequency spectrum is extracted by a peak search method, so as to obtain the rotation frequency of the rotating shaft, and obtain a rotation speed signal
The peak search process is as follows:
(1) the rotating machinery speed increasing and decreasing process always has a stable rotating speed stage, and a frequency value corresponding to the stable rotating speed is determined;
(2) taking the frequency value of the stable moment as a peak value searching starting point, and sequentially searching for peak values;
(3) ensuring that the frequency of the previous moment is not greater than (speed increasing stage) or not less than (speed decreasing stage) the frequency value of the next moment in the searching process;
(4) and (4) eliminating the special points which do not meet the condition (3) in the searching process, and combining a spline interpolation method, so that the rotating frequency of the rotating shaft can be obtained, and the rotating speed signal is obtained.
The specific process of the adaptive Vold-Kalman filtering order ratio tracking algorithm in the step three for extracting the order of a certain order signal is as follows:
(i) equation of state
a(nΔt)-2cos(ωΔt)a((n-1)Δt)+a((n-2)Δt)＝0 (1)
Wherein Δ t is a discrete time; a (n Δ t) is the nth discrete-time sample; ω is the sine wave instantaneous frequency.
Equation (1) describes a sine wave whose frequency amplitude is constant at three consecutive time points. Since the frequency of the step ratio is time-varying, it is not constant. The equation of state can be expressed by (2):
a(nΔt)-2cos(ωΔt)a((n-1)Δt)+a((n-2)Δt)＝(n) (2)
in the formula: (n) is called the non-uniform term and is used to describe the variation of the amplitude and frequency of the ideal sine wave. a (n Δ t) is expressed as the state of the nth sampling point, n sampling points exist in the state equation of the whole system, and (2) the formula is expanded as follows:
the state equation can be obtained from equation (3) in the form of a matrix:
FA＝ (4)
(ii) equation of observation
The actual measured vibration signal is composed of the sum of the components of the order ratios plus measurement error and noise, and the observation equation describes the relationship between the order ratio x (n) and the measurement data y (n). The measurement data contains not only the order of interest, but also all the order and background noise generated by the machine. The observation equation is expressed as follows:
y(n)＝x(n)+σ(n) (5)
where σ (n) is the non-tracking order ratio and random noise; x (n) is the extracted order ratio component; y ((n) is the value of the nth sample point of the measured vibration signal.
And (3) expanding an observation equation:
written in matrix form as:
y＝x+ (7)
(iii) adaptive state parameter identification recursion algorithm
First, a system for discrete control of a process is introduced, which can be described by a linear random differential equation:
a(k)＝Fa(k-1)+BU(k)+ψ(k) (8)
plus the system measurements:
Y(k)＝Ca(k)+ξ(k) (9)
in the above two equations, a (k) is the system state at time k, and u (k) is the control amount of the system at time k. F and B are system parameters, which are matrices for a multi-model system. Y (k) is the measurement at time k, and C is the observation matrix of the observation system. ψ (k) and ξ (k) represent the noise of the state equation and the observation equation, respectively. They are assumed to be white gaussian noise with covariance Q, R, respectively, assuming that they do not change with system state changes.
The kalman filter is the optimal information processor because the above conditions are satisfied (linear random differential system, both state and observation are gaussian white noise). The optimized output of the system is evaluated as follows, as shown in fig. 5.
The system for the next state is first predicted using the state transition matrix of the system. Assuming that the present system state is k, according to the model of the system, the present state can be predicted based on the last state of the system:
a(k|k-1)＝Fa(k-1|k-1)+BU(k) (10)
in the equation (10), a (k | k-1) is the result predicted by the last state, a (k-1| k-1) is the optimum result of the last state, and u (k) is the control amount of the current state, which may be 0 if there is no control amount.
The system results have been updated so far, and it may be that the covariance corresponding to a (k | k-1) has not been updated. Covariance is denoted by P:
P(k|k-1)＝FP(k-1|k-1)F′+Q (11)
in equation (11), P (k | k-1) is the covariance corresponding to a (k | k-1), P (k-1| k-1) is the covariance corresponding to a (k-1| k-1), F' represents the transposed matrix of F, and Q is the covariance of the system state.
With the prediction of the present state, the measured values of the present state are collected. Combining the predicted value and the measured value, an optimized estimated value a (k | k) of the current state (k) can be obtained:
a(k|k)＝a(k|k-1)+Kg(k)(Y(k)-Ca(k|k-1)) (12)
where Kg is the Kalman gain:
in addition, in order for the kalman filter to run to the end of the system process, the covariance of a (k | k) in the k state needs to be updated:
P(k|k)＝(I-Kg(k)C)P(k|k-1) (14)
where I is the identity matrix, I ═ 1 for the single model single measurements. When the system enters the (k +1) state, P (k | k) is P (k-1| k-1) in equation (11).
The specific method for analyzing the modal parameters of the extracted order signals by using the FSDD method in the fourth step is as follows:
as shown in fig. 6, after the order component is extracted, the order component signal is analyzed and identified by using the FSDD method, which specifically comprises the following steps: after the power spectrum of the order component is solved, an enhanced power spectrum can be obtained through calculation according to a left singular vector and a right singular vector which are obtained through singular value decomposition, and the enhanced power spectrum is approximate to a single-degree-of-freedom system, so that the natural frequency and the damping ratio can be obtained through calculation.
The singular value decomposition formula is:
[U][S][V]H＝SVD({O1}{O2}…{Om}) (15)
in the formula (15), [ U ]]Is a left singular vector matrix; [ S ]]Is a singular value diagonal matrix; [ V ]]Is a right singular vector matrix; { OiIs the power spectrum of the order component i.
The enhanced power spectrum calculation formula based on the order component is as follows:
G(jω)＝{Ul}H[{O1}{O2}…{Om}]n×m{Vl} (16)
in the formula (16), G (j ω) is an enhanced power spectrum based on the order component; { Ul}HIs the conjugate transpose of the left singular vector; { O } is the power spectrum of the order component i; { VlIs the right singular vector.
Claims (5)
1. The order extraction-based modal analysis method for the running state of the rotor of the rotary machine is characterized in that the method combines a self-adaptive filtering order ratio tracking technology with a modal identification algorithm and is used for identifying modal parameters of the rotor; firstly, extracting a vibration signal of a rotor running state based on an adaptive Vold-Kalman filtering order ratio tracking technology of instantaneous frequency estimation, and obtaining a modal parameter of the rotor through a frequency domain space domain decomposition method under the condition of only response;
the specific process of extracting the vibration signal of the rotor running state by the self-adaptive Vold-Kalman filtering order ratio tracking technology based on instantaneous frequency estimation comprises the following steps:
the method comprises the following steps: calculating the rotating speed of the rotor by using an instantaneous frequency estimation method aiming at the vibration signal of the rotor of the rotating machine;
step two: extracting an order signal by combining a self-adaptive Vold-Kalman filtering order ratio tracking technology according to the rotating speed;
the state equation takes the form of a matrix:
FA＝ (4)
the observation equation is expressed as follows:
y(n)＝x(n)+σ(n) (5)
where σ (n) is the non-tracking order ratio and random noise; x (n) is the extracted order ratio component; y (n) is the value of the nth sampling point of the actually measured vibration signal;
the specific process of obtaining the modal parameters of the rotor by the frequency domain and space domain decomposition method under the condition of only response comprises the following steps:
step 1: directly performing power spectrum analysis on the extracted certain order signal, and performing singular value decomposition on the power spectrum to obtain a left singular vector and a right singular vector;
step 2: and calculating to obtain an enhanced power spectrum according to the left singular vector and the right singular vector, and calculating the damping and the natural frequency by using the enhanced power spectrum.
2. The order-extraction-based rotating machine rotor operating state modal analysis method according to claim 1, wherein the specific process of the first step is as follows:
step 1.1, determining a frequency value corresponding to a stable rotating speed according to a stable rotating speed stage in the speed increasing and decreasing process of a mechanical rotor;
step 1.2, when the machine is stably rotated, a frequency value at a certain moment is taken as a peak value search starting point, and peak value search is sequentially carried out;
step 1.3, in the searching process, ensuring that the frequency at the previous moment is not more than the frequency value at the next moment in the speed increasing stage, and the frequency at the previous moment in the speed reducing stage is not more than or not less than the frequency value at the next moment;
and step 1.4, eliminating special points which do not meet the conditions in the step 1.3 in the searching process, and combining a spline interpolation method to obtain the rotating frequency of the rotating shaft so as to obtain a rotating speed signal.
3. The order-extraction-based rotating machine rotor operating state modal analysis method according to claim 1, wherein the specific process of the second step is as follows:
step 2.1, establishing a system model:
the state equation of the system is as follows:
a(k)＝Fa(k-1)+BU(k)+ψ(k) (8)
the system's observation equation is:
Y(k)＝Ca(k)+ξ(k) (9)
in the above two formulas, a (k) is the system state at time k, and U (k) is the control quantity of the system at time k; f and B are system parameters Y (k) are measured values at the moment k, C is an observation matrix of the observation system, psi (k) and xi (k) respectively represent noise of the state equation and the observation equation and are Gaussian white noise;
step 2.2, estimating the optimized output of the system,
firstly, predicting a system of a next state by using a state transition matrix of the system, setting that the system state is k, and predicting the present state based on the previous state of the system according to a model of the system:
a(k|k-1)＝Fa(k-1|k-1)+BU(k) (10)
in the formula (10), a (k | k-1) is the result of prediction using the previous state, a (k-1| k-1) is the optimal result of the previous state, and U (k) is the control amount of the current state;
covariance is denoted by P:
P(k|k-1)＝FP(k-1|k-1)F′+Q (11)
in the formula (11), P (k | k-1) is the covariance corresponding to a (k | k-1), P (k-1| k-1) is the covariance corresponding to a (k-1| k-1), F' represents the transposed matrix of F, and Q is the covariance of the system state;
collecting the measured value of the current state, and combining the predicted value and the measured value to obtain an optimized estimated value a (k | k) of the current state k:
a(k|k)＝a(k|k-1)+Kg(k)(Y(k)-Ca(k|k-1)) (12)
where Kg is the Kalman gain:
update covariance of a (k | k) in k-state:
P(k|k)＝(I-Kg(k)C)P(k|k-1) (14)
where I is the identity matrix.
4. The order extraction-based rotating machine rotor operating state modal analysis method according to claim 1, wherein the specific process of the step 1 is as follows:
the singular value decomposition formula is:
[U][S][V]H＝SVD({O1}{O2}L{Om}) (15)
in the formula (15), [ U ]]Is a left singular vector matrix; [ S ]]Is a singular value diagonal matrix; [ V ]]Is a right singular vector matrix; { OiIs the power spectrum of the order component i.
5. The order-extraction-based rotating machine rotor operating state modal analysis method according to claim 4, wherein the specific process of the step 2 is as follows:
the enhanced power spectrum calculation formula based on the order component is as follows:
G(jω)＝{Ul}H[{O1}{O2}L{Om}]n×m{Vl} (16)
in the formula (16), G (j ω) is an enhanced power spectrum based on the order component; { Ul}HIs the conjugate transpose of the left singular vector; { O } is the power spectrum of the order component i; { VlIs the right singular vector.
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| CN108227505B (en) * | 2018-01-30 | 2020-07-28 | 西安交通大学 | Prediction-adaptive control-based milling electric spindle vibration suppression system and method |
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